3,313 research outputs found
Two-Point Codes for the Generalized GK curve
We improve previously known lower bounds for the minimum distance of certain
two-point AG codes constructed using a Generalized Giulietti-Korchmaros curve
(GGK). Castellanos and Tizziotti recently described such bounds for two-point
codes coming from the Giulietti-Korchmaros curve (GK). Our results completely
cover and in many cases improve on their results, using different techniques,
while also supporting any GGK curve. Our method builds on the order bound for
AG codes: to enable this, we study certain Weierstrass semigroups. This allows
an efficient algorithm for computing our improved bounds. We find several new
improvements upon the MinT minimum distance tables.Comment: 13 page
AG codes and AG quantum codes from the GGS curve
In this paper, algebraic-geometric (AG) codes associated with the GGS maximal
curve are investigated. The Weierstrass semigroup at all -rational points of the curve is determined; the Feng-Rao designed
minimum distance is computed for infinite families of such codes, as well as
the automorphism group. As a result, some linear codes with better relative
parameters with respect to one-point Hermitian codes are discovered. Classes of
quantum and convolutional codes are provided relying on the constructed AG
codes
Two-point AG codes from one of the Skabelund maximal curves
In this paper, we investigate two-point Algebraic Geometry codes associated
to the Skabelund maximal curve constructed as a cyclic cover of the Suzuki
curve. In order to estimate the minimum distance of such codes, we make use of
the generalized order bound introduced by P. Beelen and determine certain
two-point Weierstrass semigroups of the curve.Comment: 15 page
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